The base of the isosceles triangle is parallel to x -axis and has both end-points on the parabola y =x(10-x)and its vertex belongs to the x -axis. Find area of the triangle if t…

Question

The base of the isosceles triangle is parallel to x -axis and has

both end-points on the parabola
`y =x(10-x)`and its vertex
belongs to the x -axis. Find area of the triangle if the length of its
base is 8.

Answer 1

36 square units

Explanation:

y = x(10-x)

This is a down-opening parabola with axis of symmetry x = 5

Vertex of triangle (5,0)

Base of triangle is the horizontal chord of length 8, endpoints x = (1,9) and (9,9).

Height of triangle = 9

Area of triangle = ½·8·9 = 36 square units